* Corresponding author: r.sochaczewski@pollub.pl

Numerical Analysis of a Fuel Pump for an Aircraft Diesel Engine

Rafał Sochaczewski1*, and Marcin Szlachetka2

1 Lublin University of Technology, Faculty of Mechanical Engineering, Nadbystrzycka 36, 20-618 Lublin, Poland 2 Pope John Paul II State School of Higher Education, Department of Mechanical Engineering, ul. Sidorska 95/97, 21-500 Biala

Podlaska, Poland

Abstract. The paper reports on the process of modelling a high-pressure common rail pump designed to

supply a two-stroke compression-ignition engine, which includes the presentation of methodology for

model construction and results of simulation tests. A one-dimensional model of the pump was developed

in the AVL Hydsim environment. A single-section positive displacement pump driven by a double cam

was used for modelling. The developed model enables simulation of pump operation in various conditions

defined by shaft speed, pumping pressure, settings of pump executive elements as well as fuel properties.

The obtained results were compared with the results of bench tests and theoretical calculations. The

analysis included the flow rate fuel overflow and changes in pumping pressure depending on the fuel

dispenser settings. The model will also be used to build a complete fuel supply system model consisting

of an injector model, a rail model and a control system model. The research is carried out with a view to

optimising individual components and the operation of the entire supply system, taking into account the

regulation of pumping pressure and synchronisation of the pumping process with fuel injection cycles.

1 Introduction

Increasing requirements to reduce exhaust emissions and

fuel consumption while not compromising the power

factor is currently becoming widely applicable to internal

combustion engines intended for aircraft applications. As

a result, intensive research works are underway to develop

a diesel-powered unit for aircraft propulsion. The paper

[1] discusses the parameters of about 40 types of aircraft

diesel engines. Due to a number of advantages, such as:

lack of the head (lower heat loss) and timing system,

opposite movement of pistons conducive to balancing the

engine, development and modernisation of the

compression-ignition engine operating in a two-stroke

cycle and opposing pistons, the design was subjected to

development and modernisation [2, 3, 4]. Of course, such

a construction also has drawbacks. The main one is the

need for the use of a gear connecting two crankshafts or a

complicated crank system with one shaft. Due to the

specific pistons-sleeves arrangement, it is necessary to

place the injector or fuel injectors perpendicularly to the

cylinder axis. As a result, it is necessary to develop a new

combustion chamber and a power supply system

cooperating with this chamber.

In order to facilitate optimisation and limit the number

of experiments, numerical modelling analyses are used.

Scientific literature describes numerous modelling tests of

fuel system elements [5, 6, 7, 8] as well as entire injection

systems [9, 10, 11, 12, 13]. By way of illustration, [5]

investigated the effect of multiphase injection on the

emission of particulate matter and nitrogen oxides, works

[6, 7] included micro and macroscopic dynamic

phenomena accompanying multiphase injection, whereas

[8, 11, 14] – the effect of cavitation on flow loss.

Mathematical modelling is a method often used in the

design and testing of aircraft engines. It helps shorten the

time from concept to prototype, as in the case with the

following models of: the process of combustion [15, 16],

cooling systems [1716, 18], charge exchange [19], or

whole engines [20, 21].

The paper [22] presents the process of electromagnetic

modelling of the common rail injector. The employed

computational method optimised the fuel nozzle installed

in a commercial injector for use in a two-stroke diesel

engine. In order to simulate the operation of the complete

fuel system, in the next stage a model of a high-pressure

pump was made, which was the primary subject of the

work. The model was developed by means of BOOST-

Hydsim software tool by AVL– an environment for

analysis of fuel supply systems. The module in question

is dedicated to dynamic analysis of hydraulic and hydro-

mechanical systems and control systems [23, 24, 25, 26].

It is based on the theory of fluid dynamics and vibration

of multi-member systems.

This article presents the process of modelling a high-

pressure pump for a two-stroke compression-ignition

engine and opposing pistons. The engine is at the design

stage; the assumed power is 100 kW and capacity 1500

cm3. The objective of the study is to optimise the pump

flow rate in order to supply the engine in all operating

conditions, as well as to develop a complete supply

system in order to carry out further optimisation works.

© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0

(http://creativecommons.org/licenses/by/4.0/).

MATEC Web of Conferences 252, 01003 (2019) https://doi.org/10.1051/matecconf/201925201003CMES’18

2 Materials and methods

2.1 AVL BOOST Hydsim

BOOST Hydsim is a module dedicated to dynamic

analysis of hydraulic and hydro-mechanical systems and

control systems. It is based on the theory of fluid

dynamics and vibration of multi-member systems.

Originally, the program was developed to simulate

injection systems of compression-ignition engines. At the

moment, it enables modelling of petrol, heavy oils and

alternative fuels supply systems. In addition, it is

supplemented with new applications such as hydraulic

transmissions, control of valves and actuators. It can be

used to simulate multi-phase injection and systems

containing control units.

BOOST Hydsim is an integral tool in the AVL

Workspace equipped with a graphical pre-processing

editor. The one-dimensional model presented in BOOST

Hydsim contains a general image of the system, defined

by the user. Models are built from elements grouped

depending on their type and functionality. Each specific

element of the physical supply system is represented by

an icon, a symbol containing a schematic drawing of the

element on the GUI (Graphical User Interface). System

elements (icons) can be connected with each other by

mechanical, hydraulic or logical connections. Thanks to

this solution, it is possible to define the supply system in

any configuration of component connections. The GUI

controls the model building process and prevents

connections that do not conform to the input specification.

Input data depends on the configuration of the system

and a specific calculation task (standard calculation,

restart, run with optimisation or serial calculations). A

fixed set of input parameters is associated with each

element. Some parameters are optional, realised by means

of switches. Each element has an identification number

and user name. Fluid properties and mechanical

connections require separate inputs. In addition, general

model calculation control data must be specified.

Each element has a defined set of results, which, after

being selected by the user, are stored in ASCII files.

Default data and control information are stored in a GIDas

file. Its content can be opened directly in Case Explorer,

which is integrated with Impress Chart post-processor.

An iteration history file (GAD File) is created to run the

optimisation. Two tools are used to present simulation

results: IMPRESS Chart (allows the user to generate

charts using predefined templates or designed by the user)

and PP3 (for flow animations) [15, 16].

2.2 Assumptions of the model

The model was developed in an environment with

libraries allowing building a structure of any fuel supply

system. The model calculates fuel parameters in particular

elements of the fuel pump. This enables visualising

simulation results in the form of flow parameters for

hydraulic (pressure, temperature, volume or mass flow,

geometric and effective flow surface, flow resistance,

steam bubbles, cavitation coefficient) and mechanical

elements (coordinates, speed, acceleration, dynamic

forces and torque, kinematic parameters). Calculation

results are available in the time domain or crankshaft

rotation angle.

During the construction of the pump model, the

following assumptions and simplifications resulting from

the specific operation of the program (dimensionality of

the mathematical model) were made:

a one-dimensional model taking into account only the

length and diameter of the flow elements,

the high-pressure pump is a piston displacement pump,

the pumping sections of the high-pressure pump are

geometrically identical,

the geometric orientation of the elements of the system

has no influence on their operation,

the temperature of the walls of the components is

constant,

fuel flow through pump components includes circular

cross-section components,

the boundary mechanical condition defines a position

or velocity in one direction only and is a fixed value,

elements of the pump are assumed to be non-

deformable elements (coordinates and piston velocity

between the input and output state are the same),

volumes are elements with non-deformable walls,

the volumes were connection by cylinders taking into

account the frictional losses determined by the Laplace

transform,

33 % of the mass of the spring is added to the mass of

the moving elements affected by the spring.

2.3 Test object

The CP4 series pump (Fig. 1), next version of the Bosch

high-pressure pump, was used for the calculation.

Compared to the previous generation, the design has been

optimised by reducing the number of components and the

application of aluminium pump housing. High fuel

pressure is generated in the pumping section and is flows

directly through high-pressure pipe to the rail - there are

no high-pressure fuel channels in the body. It is a single-

section positive displacement pump (CP 4.1) driven by a

cam roller with a double cam. The pump flow rate is

regulated by a dosing valve located in the pump body. The

pump has a flange mounting and the possibility of placing

a gear wheel on the pump shaft. This makes it possible to

install the pump in an engine block and transfer the drive

from the gearing. The pump is supplied with fuel by

means of a low-pressure electric pump. Pre-pressure is

stabilised by means of a bypass valve in the range of 0.45

to 0.5 MPa. The pump is lubricated with fuel. Depending

on the number of pumping sections, the drive ratio is 1:1

or 1:2.

Fig. 1. CP4.1 pump.

2

MATEC Web of Conferences 252, 01003 (2019) https://doi.org/10.1051/matecconf/201925201003CMES’18

2.4 Pump model

Based on the geometry of the CP4.1 pump, a pump model

was built in the AVL BOOST-Hydsim. A schematic of

the pump model is shown in Fig. 2.

Fig. 2. Scheme of the CP 4.1 pump model.

The high-pressure pump model consists of three

blocks. The first block is the pump drive block. This is a

shaft double cam roller model. At the bottom of the pump

there is a cam drive (S) for which the rpm has been

defined. The shaft is mounted in the pump casing at two

points. The boundary mechanical conditions (B_M_1 and

B_M_2) deprived the drive shaft of its degrees of freedom

and gave it a rotary motion (R/16).

The unit vector of the x-axis of the element in the

global coordinate system is determined from the equation:

𝑋𝑙𝑜𝑘 = 𝑒1𝑋𝑔𝑙

+ 𝑒2𝑌𝑔𝑙 + 𝑒3𝑍𝑔𝑙

(1)

where: 𝑋𝑔𝑙 , 𝑌𝑔𝑙

, 𝑍𝑔𝑙 are unit vectors in the global

coordinate system, e1, e2, e3 are the unit vector

components in the global x, y and z direction. Default

values for unit vector are 1. / 0. / 0. (global and local

coordinate systems are identical).

The cam (Cam/12) of the pumping section is located

on the drive shaft. The setting window allows the user to

define the profile of the cam. The window defines the

radius of the basic cam circle, the displacement of the

tappet relative to the axis of rotation, the lift and initial

speed of the tappet, the angular displacement of the cam

relative to the beginning of the calculation. The profile of

the cam can be defined by lift or acceleration as a function

of shaft rotation.

In the modelled pump, the profile of the cam was

defined by introducing lift as a function of shaft rotation.

The cam lift was measured (Table 1) and its

characteristics were determined (Fig. 3).

Table 1. Pump cam lift values CP4.1.

No Angle Lift No Angle Lift

[deg] [mm]

[deg] [mm]

1 0.00 0.000 25 180.00 0.000

2 7.50 0.192 26 187.50 0.207

3 15.00 0.710 27 195.00 0.727

4 22.50 1.460 28 202.50 1.444

5 30.00 2.345 29 210.00 2.356

6 37.50 3.319 30 217.50 3.293

7 45.00 4.191 31 225.00 4.220

8 52.50 5.088 32 232.50 5.115

9 60.00 5.845 33 240.00 5.892

10 67.50 6.520 34 247.50 6.519

11 75.00 7.027 35 255.00 7.030

12 82.50 7.344 36 262.50 7.369

13 90.00 7.433 37 270.00 7.439

14 97.50 7.304 38 277.50 7.300

15 105.00 6.966 39 285.00 6.957

16 112.50 6.399 40 292.50 6.399

17 120.00 5.696 41 300.00 5.680

18 127.50 4.880 42 307.50 4.885

19 135.00 4.006 43 315.00 4.003

20 142.50 2.986 44 322.50 3.108

21 150.00 2.090 45 330.00 2.139

22 157.50 1.236 46 337.50 1.263

23 165.00 0.544 47 345.00 0.547

24 172.50 0.086 48 352.50 0.114

Fig. 3. Profile of the CP4.1 pump drive shaft cam.

The components in the pump drive block are

connected by mechanical bonds with a defined connection

direction, preload, stiffness and damping.

The second block is a pumping section block which is

connected to the pump drive block by means of

mechanical bonds (movement of the piston with a

displacement caused by rotation of the cam). The

pumping section block contains: an axial pump (P_1/1 -

piston with cylinder), volume over piston (C_V_1/5 -

compression chamber) as well as an inlet valve (I_V_1/8)

and an outlet valve (0_V_1/6). The pumping section is

non-deformable and is defined by the mass in progressive

motion, piston diameter, friction force, pressure in the

3

MATEC Web of Conferences 252, 01003 (2019) https://doi.org/10.1051/matecconf/201925201003CMES’18

piston chamber and spring parameters in the pumping

section.

The pumping section is connected by a hydraulic line

with a compression chamber of a preset volume to which

a ring gap (L_1/7) is connected. The function of this

element is to model fuel leaks between the cooperating

elements of the pumping section. For this reason, the

leakage is connected to the pump (element P_1/1) by a

special functional connection. This means that both

elements are parts of a certain physical unit. Each leak is

defined by the initial fixed leakage length and the gap

between the piston and cylinder as a function of pressure.

Fuel from the pumping section is channelled through

a (P_V/3) channel located in the pumping section to the

stub pipe connecting the pump with the rail.

The leakage model is based on the Hagen-Poiseuille

law. It considers steady laminar flow through annular gap

because small cross-sectional gap area results in laminar

flow. As fluid enters the annular gap, the velocity profile

is linear. The fluid velocity at the barrel wall is equal to

barrel velocity and at the piston wall is equal to piston

velocity. This layer of fluid exerts considerable shear

forces on the inner layers whose velocities must exceed

the piston velocity vp to satisfy the law of continuity. In

the case of constant laminar flow through the ring gap, the

Navier-Stokes equation takes the form of:

𝑑𝑝

𝑑𝑥= 𝜇

𝑑2𝑣

𝑑𝑦2 (2)

where: x, y – coordinates of motion, v – fluid velocity in

x direction, p – pressure μ – dynamic viscosity.

Flow rate through leakage gap is defined by:

(3)

where: pin. pout – pressure on input/output side of piston,

Lgap – gap length, Rb. Rp – radius of barrel/piston, vb. vp –

velocity of barrel/piston.

Inlet and outlet valves are defined by: masses in

progressive motion, maximum lift, coefficient of flow

resistance through the valve at the largest opening of the

valve, pressure differences for valve opening. Parameters

of valve seat and valve spring were also determined. in the

adopted linear model of a valve in the seat stiffness and

damping are constant, and at positive distances there is no

clamping force.

The motion of the valve masses in the local coordinate

system is given by the equation:

𝑚�� + 𝑐0 �� + 𝑘0𝑥 = −𝐹0 −𝐹ℎ𝑦𝑑 − 𝐹𝑑𝑎𝑚𝑝 −𝐹𝑖𝑛𝑠𝑡 −𝐹𝑜𝑢𝑡𝑠𝑡 (4)

where: m – valve mass, x – valve coordinate, c0. k0 –

damping and stiffness constants of the valve spring, F0 –

preload force of the valve spring, Fhyd – hydraulic force,

Fdamp – damping force of squeezing fluid at valve closing,

Fin_st. Fout_st – additional forces from input and output

stops.

The third block is the part of the pump responsible for

supplying fuel to the pumping section and removing fuel

from the pump. Fuel for pumping sections is delivered

from a low pressure system defined by boundary

conditions F/10 by determining temperature and pressure

of medium as a function of time (optional rotation angle).

Fuel flows through line (/21) to a flow control orifice

(S_T/24 - orifice simulates the operation of the dispenser

of fuel) and then the volume I_V_1/25 and I_V_2/9 goes

to the pumping section. Excess fuel from the pump is

directed to the low-pressure part of the system specified

by L conditions.

Hydraulic boundary conditions were assumed for the

calculations: F/10 corresponds to the parameters of fuel

supplied to the pumping sections: pressure 0.3 MPa and

temperature 313 K; L - overflow of fuel: pressure 0.1 MPa

and temperature 313 K; L_R - fuel pumped to the rail:

pressure from 30 to 140 MPa, temperature 323 K. The fuel

used is diesel oil with a density of 850 kg/m3 and

temperature and pressure corresponding to boundary

conditions.

3 Results

This section presents the results from simulation studies.

In the first stage the numerical results were compared with

available results obtained from bench tests. Fig. 4 presents

a comparison of pump output obtained from model

(Hydsim), bench tests and theoretical calculations – based

on the size of the pumping section. The pump output

obtained from model tests was the sum of volumetric flow

rate of fuel from the pumping section and fuel from

section leaks. It was assumed that the fuel dispenser is

fully open and the rotational speed of the pump shaft

changed. The pumping pressure was assumed to be 30

MPa. The most significant differences in flow rates are for

the pump shaft speed of 2500 rpm, which amounts to

approx. 2.5 %. As the speed decreases, the difference

decreases to about 1.5 %.

Fig. 4. Flow rate characteristics of CP4.1 pump (Hydsim,

theoretical and bench tests).

Fig. 5 shows a comparison of the pumping pressure

during one rotation of the pump shaft. The pressure

waveforms exhibit slight differences, which may be

attributed to the fact that in the model the preset pressure

in the reservoir was regulated by means of a check valve,

while in the case of bench tests - by means of a bleed valve

controlled by the PID regulator. However, the pressure

ranges are comparable.

4

MATEC Web of Conferences 252, 01003 (2019) https://doi.org/10.1051/matecconf/201925201003CMES’18

Fig. 5. Pressure waveform (Hydsim, bench tests).

For the same operating conditions, the torque

waveform and amplitude on the pump shaft (Fig. 6) were

compared.

Fig. 6. Torque waveform (Hydsim, bench tests).

In the next stage, tests simulating the operation of the

dosing device regulating the amount of incoming fuel to

the pumping section were carried out. The function of the

dispenser is performed by an orifice (S_T/24) with

adjustable flow cross-sectional area. The flow field

changed from 0.25 mm2 to 1.00 mm2 at 0.25 mm2 steps.

As the flow area field decreases, the flow rate (Fig. 7) and

the amount of leakage through the pumping section (Fig.

8) decreases. The pumping rate decreases by approx.

32%. and leaks by approx. 20%.

Flow throttling causes the pumping section to become

filled only partially. Fig. 9 shows the pressure in the

pumping section chamber. There is a delay in pumping

due to throttling the flow of fuel flowing into the pumping

section and as a result the piston stroke is reduced and the

shaft contact with the pusher is delayed.

Fig. 7. Volume of fuel flowing out of the pumping section

depending on the orifice size.

Fig. 8. Volume of fuel flowing through the leakage depending

on the orifice size.

Fig. 9. Pressure waveforms in the pumping section chamber

C_V_1/5.

Fig. 10. Pressure waveforms in the discharge section chamber

C_V_1/5 on a narrow scale.

Fig. 10 shows the changes in a narrow scale of the

rotation angle of the pump drive shaft. The differences in

the discharge delay are maximum 20% for a flow area

from 0.25 to 0.75 mm2, whereas above 0.75 mm2 no

differences in the pressure curve were observed, which

means that the volume of the delivery section is

completely filled with fuel.

4 Conclusions

The developed numerical model of the common rail high-

pressure pump gives relatively good results, comparable

with bench tests and theoretical calculations. The model

will be used for optimisation tests of the pump and

cognitive dynamic, cavitation, etc. phenomena occurring

during the flow of liquid through the pump elements,

especially at high pressures.

The model will furthermore be applied in the

construction of the entire power supply system for a two-

stroke diesel engine with opposing pistons. The research

will optimise the work of the injector as well as the control

algorithm in terms of pressure regulation and

synchronisation of the pumping process with fuel

injection cycles.

5

MATEC Web of Conferences 252, 01003 (2019) https://doi.org/10.1051/matecconf/201925201003CMES’18

In relation to the obtained simulation results, the

model needs certain modifications. This will require

additional experimental tests and calibration of the model.

This work has been realised in cooperation with the

Construction Office of WSK "PZL-KALISZ" S.A." and is part

of Grant Agreement No. POIR.01.02.00-00-0002/15 financed

by the Polish National Centre for Research and Development.

References

1. M. Gęca Michał, Z. Czyż, M. Sułek, Combustion

Engines, 169 (2017)

2. J. Pirault, M. Flint, SAE (2009)

3. J. Heywood, (1988)

4. M. Franke, H. Huang, J. Liu, SAE (2006)

5. V. Amoia, A. Ficarella, D. Laforgia, S. De Matthaeis,

SAE (1997)

6. G. Bianchi, P. Pelloni, F. Corcione, F. Luppino, SAE

(2001)

7. L. Catalano, V. Tondolo, A. Dadone, SAE (2002)

8. A. Ficarella, D. Laforgia, V. Landriscina, SAE

(1999)

9. C. Gautier, O. Sename, L. Dugard, G. Meissonnier,

IFAC (2005)

10. P. Lino, B. Maione, A. Pizzo, Appl Math Model

(2007)

11. R. Payri, H. Climent, F. Salvador, P I Mech Eng D-J

AUT (2004)

12. X. Seykens, L. Somers, R. Baer, MECCA (2005)

13. X. Seykens, L. Somers, R. Baer, VAFSEP (2004)

14. C. Arcoumanis, M. Gavaises, E. Abdul-Wahab, V.

Moser, SAE (1999)

15. Z. Czyż, K. Pietrykowski, Adv. Sci. Technol. Res. J.,

8 (2014)

16. A. Nazarewicz, K. Pietrykowski, M. Wendeker, J.

Czarnigowski, P. Jakliński, M. Gęca, PTNSS

CONGRESS, SC2 (2007)

17. K. Pietrykowski, T. Tulwin, SAE, 8 (2015)

18. Ł. Grabowski, Z. Czyż, K. Kruszczyński, SAE 2014-

01-2883 (2014)

19. Ł. Grabowski, K. Pietrykowski, P. Karpiński, ITM

WEB OF CONFERENCES, 15 (2017)

20. Z. Czyż, Ł. Grabowski, K. Pietrykowski, J.

Czarnigowski, M. Porzak, Measurement, 113 (2018)

21. P. Magryta, K. Pietrykowski, M. Gęca, Transactions

of the Institute of Aviation, 250 (2018)

22. R. Sochaczewski, Z. Czyż, K. Siadkowska,

Combustion Engines 170 (2017)

23. AVL BOOST Hydsim Primer, (2013)

24. AVL BOOST Hydsim User Guide (2013)

25. V. Caika, P. Sampl, SAE (2011)

26. A. Pirooz, Indian J.Sci.Res., 5 (2014)

6

MATEC Web of Conferences 252, 01003 (2019) https://doi.org/10.1051/matecconf/201925201003CMES’18